Metamaterial phase shifters

ABSTRACT

The present technology pertains to a system and method of operation of a metamaterial phase shifter having various use applications. In one aspect of the present disclosure, a phase shifter includes a network of tunable impedance elements and a controller. The controller is coupled to the network of tunable impedance elements and configured to receive a phase shift input value and determine a corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based on the phase shift input value, the network of tunable impedance element being configured to shift a phase of an input signal based on tuning voltages supplied to the network of tunable impedance elements by the controller.

If an Application Data Sheet (ADS) has been filed on the filing date ofthis application, it is incorporated by reference herein. Anyapplications claimed on the ADS for priority under 35 U.S.C. §§ 119,120, 121, or 365(c), and any and all parent, grandparent,great-grandparent, etc., applications of such applications are alsoincorporated by reference, including any priority claims made in thoseapplications and any material incorporated by reference, to the extentsuch subject matter is not inconsistent herewith.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of the earliest availableeffective filing date(s) from the following listed application(s) (the“Priority Applications”), if any, listed below (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC § 119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Priority Application(s)).

PRIORITY APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/807,338, filed Nov. 8, 2017, for METAMATERIAL PHASE SHIFTERS, withinventor Yaroslav Urzhumov, which is incorporated herein by reference inits entirety.

TECHNICAL FIELD

The present technology pertains to a system and method of operation of ametamaterial phase shifter having various use applications including,but not limited to, antenna systems.

BACKGROUND

A phase shift module or a phase shifter is a device that receives aninput signal such as a radio frequency electromagnetic signal andprovides a controllable shift of the phase of the input signal. Atmicrowave frequencies, phase shifters are usually implemented asmicrowave networks—electromagnetic circuits composed of transmissionlines and various circuit elements, including controllable (tunable)elements. Phase shifters can be classified as active or passive,depending on whether signal magnitude is amplified. Phase shifters canbe also classified as analog or digital, depending on whether theyprovide a continuous range or a discrete set of possible phase shifts.Example applications of phase shifters include phased array antennas,including electronically steerable arrays (ESA), software-definedantennas (SDA) and so on.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which the above-recited and otheradvantages and features of the disclosure can be obtained, a moreparticular description of the principles briefly described above will berendered by reference to specific embodiments thereof, which areillustrated in the appended drawings. Understanding that these drawingsdepict only exemplary embodiments of the disclosure and are nottherefore to be considered to be limiting of its scope, the principlesherein are described and explained with additional specificity anddetail through the use of the accompanying drawings in which:

FIG. 1 illustrates a phase shift module, according to one aspect of thepresent disclosure;

FIG. 2 illustrates a controller of the phase shift module, according toan aspect of the present disclosure;

FIG. 3A illustrates a network of tunable impedance elements, accordingto one aspect of the present disclosure;

FIG. 3B illustrates a close-up view of a single tunable impedanceelement of network of tunable impedance elements of FIG. 1, according toan aspect of the present disclosure; and

FIG. 4 is a flow chart of a method of operation of the phase shiftmodule, according to one aspect of the present disclosure.

DETAILED DESCRIPTION

Various examples of the disclosure are discussed in detail below. Whilespecific implementations are discussed, it should be understood thatthis is done for illustration purposes only. A person skilled in therelevant art will recognize that other components and configurations maybe used without parting from the spirit and scope of the disclosure.

References to one or an example embodiment in the present disclosure canbe, but not necessarily are, references to the same example embodiment;and, such references mean at least one of the example embodiments.

Reference to “one example embodiment” or “an example embodiment” meansthat a particular feature, structure, or characteristic described inconnection with the example embodiment is included in at least oneexample of the disclosure. The appearances of the phrase “in one exampleembodiment” in various places in the specification are not necessarilyall referring to the same example embodiment, nor are separate oralternative example embodiments mutually exclusive of other exampleembodiments. Moreover, various features are described which may beexhibited by some example embodiments and not by others. Similarly,various features are described, which may be features for some exampleembodiments but no other example embodiments.

The terms used in this specification generally have their ordinarymeanings in the art, within the context of the disclosure, and in thespecific context where each term is used. Alternative language andsynonyms may be used for any one or more of the terms discussed herein,and no special significance should be placed upon whether or not a termis elaborated or discussed herein. Synonyms for certain terms areprovided. A recital of one or more synonyms does not exclude the use ofother synonyms. The use of examples anywhere in this specificationincluding examples of any terms discussed herein is illustrative only,and is not intended to further limit the scope and meaning of thedisclosure or of any exemplified term. Likewise, the disclosure is notlimited to various examples given in this specification.

Without intent to limit the scope of the disclosure, examples ofinstruments, apparatus, methods and their related results according toexamples of the present disclosure are given below. Note that titles orsubtitles may be used in the examples for convenience of a reader, whichin no way should limit the scope of the disclosure. Unless otherwisedefined, technical and scientific terms used herein have the meaning ascommonly understood by one of ordinary skill in the art to which thisdisclosure pertains. In the case of conflict, the present document,including definitions will control.

Although the terms first, second, etc. may be used herein to describevarious elements, these elements should not be limited by these terms.These terms are only used to distinguish one element from another. Forexample, a first element could be termed a second element, andsimilarly, a second element could be termed a first element, withoutdeparting from the scope of this disclosure. As used herein, the term“and/or,” includes any and all combinations of one or more of theassociated listed items.

When an element is referred to as being “connected,” or “coupled,” toanother element, it can be directly connected or coupled to the otherelement or intervening elements may be present. By contrast, when anelement is referred to as being “directly connected,” or “directlycoupled,” to another element, there are no intervening elements present.Other words used to describe the relationship between elements should beinterpreted in a like fashion (e.g., “between,” versus “directlybetween,” “adjacent,” versus “directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularexamples only and is not intended to be limiting. As used herein, thesingular forms “a”, “an”, and “the” are intended to include the pluralforms as well, unless the context clearly indicates otherwise. It willbe further understood that the terms “comprises”, “comprising,”,“includes” and/or “including”, when used herein, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Specific details are provided in the following description to provide athorough understanding of examples. However, it will be understood byone of ordinary skill in the art that examples may be practiced withoutthese specific details. For example, systems may be shown in blockdiagrams so as not to obscure the examples in unnecessary detail. Inother instances, well-known processes, structures and techniques may beshown without unnecessary detail in order to avoid obscuring examples.

In the following description, illustrative examples will be describedwith reference to acts and symbolic representations of operations (e.g.,in the form of flow charts, flow diagrams, data flow diagrams, structurediagrams, block diagrams, etc.) that may be implemented as programservices or functional processes include routines, programs, objects,components, data structures, etc., that perform particular tasks orimplement particular abstract data types and may be implemented usinghardware at network elements. Non-limiting examples of such hardware mayinclude one or more Central Processing Units (CPUs), digital signalprocessors (DSPs), application-specific-integrated-circuits, fieldprogrammable gate arrays (FPGAs), computers or the like.

Additional features and advantages of the disclosure will be set forthin the description which follows, and in part will be obvious from thedescription, or can be learned by practice of the herein disclosedprinciples. The features and advantages of the disclosure can berealized and obtained by means of the instruments and combinationsparticularly pointed out in the appended claims. These and otherfeatures of the disclosure will become more fully apparent from thefollowing description and appended claims, or can be learned by thepractice of the principles set forth herein.

OVERVIEW

In one aspect of the present disclosure, a phase shifter includes anetwork of tunable impedance elements and a controller. The controlleris coupled to the network of tunable impedance elements and configuredto receive a phase shift input value and determine a correspondingtuning voltage to be supplied to each tunable impedance element of thenetwork of tunable impedance elements based on the phase shift inputvalue, the network of tunable impedance element being configured toshift a phase of an input signal based on tuning voltages supplied tothe network of tunable impedance elements by the controller.

In one aspect of the present disclosure, a method includes receiving aphase shift input value, determining a set of voltage control signalsbased on the phase shift input value and transmitting the set of voltagecontrol signals to a network of tunable impedance elements to shift aphase of an input signal to the phase shifter such that a magnitude ofan output signal of the phase shifter and a magnitude of the inputsignal to the phase shifter are substantially similar.

DESCRIPTION

The disclosed technology is directed to the use of a network of tunableimpedance elements in a phase shift module that is configured to changea phase of an input signal.

FIG. 1 illustrates a phase shift module, according to one aspect of thepresent disclosure. As shown in FIG. 1, a phase shift module 100 (whichmay also be referred to as phase shifter 100) has an input port 102,control port 104, output port 106, controller 108 and a network oftunable impedance elements (network of T.I.E.) 110.

Phase shift module 100 has a housing that can be made of metal, plastic,etc. Input port 102 can be metallic or plastic for example. Phase shiftmodule 100 can be a digital phase shift module. In another example,phase shift module 100 can be a single input-single output digital phaseshift module.

Input port 102 can be such that a cable such as cable 112 can be screwedinto, snapped into, attached to (magnetically for example), etc. Cable112 can be any known or to be developed co-axial, etc., cable or wirecapable of transmission of signals (e.g., radio frequency signals).

Control port 104 can have one or more pins for connection to an externalcomponent through which various commands for programming of controller108 and overall operation of phase shift module 100 can be sent to phaseshift module 100. For example, control port 104 can be a 16 pin inputport with each pin having a specific function/purpose. For example, pin0 can be ground, pin 1 can be input voltage, one or more pins can eachdesignate a specific phase shift input value (e.g., 10 degrees, 30degrees, 90 degrees, 180 degrees, 270 degrees, etc.), one or more pinscan designate an operational frequency of phase shift module 100 from anoperational bandwidth range (e.g., 0 to 18 GHz, etc.). Accordingly,phase shift module 100 can be a multiple-frequency device with anoperational frequency selectable from such operational bandwidth rangeor alternatively, can be a single frequency device. In one example,phase shift module 100 is a finite-operational-bandwidth device, theoperational frequency of which is selectable from an operation bandwidthrange.

Output port 106 can be such that a cable such as cable 114 can bescrewed into, snapped into, attached to (magnetically for example), etc.Cable 114 can be any known or to be developed co-axial, etc., cable orwire capable of transmitting a signal (e.g., a radio frequency (RF)signal), the phase of which has been shifted by phase shift module 100to an intended destination depending on specific application to whichphase shift module 100 is applied.

Each one of controller 108 and network of tunable impedance elements 110will be further described with reference to FIGS. 2 and 3, respectively.

FIG. 2 illustrates a controller of the phase shift module, according toan aspect of the present disclosure. As shown in FIG. 2, controller 108can have a processor 200 and a memory 202. Memory 202 can havecomputer-readable instruction stored therein, which when executed byprocessor 200, transforms the processor 200 into a special purposeprocessor to perform functionalities for implementing a metamaterialbased phase shifter, as will be further described below with referenceto FIG. 4.

Furthermore, controller 108 can have one or more connection ports suchas connection ports 204 and one or more connection ports 206 forcommunication with control port 104 and network of tunable impedanceelements 110. Number of connection ports 204 and 206 are not limited tothat shown in FIG. 2 and instead can be more or less. However, there isat least one of each control port 204 and 206.

For example, connection port 204 can be connected to control port 104for receiving various commands such as input voltage, designated(requested) phase shift to be applied to an input signal, etc. Inanother example, connection port 206 is used to communicate variousvoltages (as will be described below with reference to FIG. 4) tonetwork of tunable impedance elements 110. One or more connection port206, as shown in FIG. 2 can be a plurality of control lines connectingcontroller 108 to network of tunable impedance elements 110. In oneexample, each of plurality of control lines 206 couples controller 108to one tunable impedance element of network of tunable impedanceelements 110.

Controller 108 can be a special purpose digital device, such asapplication-specific integrated circuits (ASIC), programmable arraylogic (PAL), programmable logic array (PLA), programmable logic device(PLD), field programmable gate array (FPGA), or other customizableand/or programmable device. Controller 108 can be installed on/attachedto a printed circuit board (PCB) inside a housing of phase shift module100. In such case, connections ports 204 and 206 can be one or more pinsof an ASIC or FPGA connected to a common conductive line on the PCB forconnection to respective one of input port 104, network of tunableimpedance elements 110, etc.

Memory 202 can be any one of, but not limited to, a non-volatile memory,static RAM, dynamic RAM, ROM, CD-ROM, disk, tape, magnetic, optical,flash memory, or other machine-readable storage medium. Various aspectsof certain embodiments may be implemented using hardware, software,firmware, or a combination thereof.

FIG. 3A illustrates a network of tunable impedance elements, accordingto one aspect of the present disclosure.

As shown in FIG. 3A, network of tunable impedance elements 110 can beassociated with variable lumped impedance elements, Zn, 303 according toan aspect of the present disclosure.

In one example, a number of tunable impedance elements of network oftunable impedance elements 110 are proportional to a number of phaseshift input values in a set of possible (available) phase shift inputvalues of phase shift module 100, from which the phase shift input valueis selected.

In another example, the number of tunable impedance elements of networkof tunable impedance elements 110 is at least equal to twice the numberof the phase shift input values.

In one example, each of the phase shift values are equally spaced on the[0, 2π] interval. In one example, each of the phase shift input valuesare distributed on the [0, 2π] interval in accordance with roots of aLegendre polynomial of a corresponding order.

Tunable metamaterials of network of tunable impedance elements 110,including two-dimensional metasurface devices, may comprise an array ofunit cells. Each unit cell can have one or more variable impedanceelements. Each impedance element or group of impedance elements may bevariably controlled based on one or more impedance control inputs(control signals (tuning voltage values/inputs) received from controller108, as will be described below). The tuning may be a one-time statictuning that is performed during the manufacturing of the antenna device,or the tuning may be a dynamic process that occurs during operation bymodifying one or more control inputs (e.g., one or more requested phaseshift value).

As an example of static tunability, a metamaterial device may bemanufactured using a 3D printer and the tuning may comprise selecting amaterial or combination of materials that results in a specificelectromagnetic or electrical property for each of the impedanceelements. Therefore, each tunable impedance element of network oftunable impedance elements 110 can be said to be formed ofelectromagnetic metamaterial.

By uniquely selecting the material or combination of materials for eachof the unit cells, a metamaterial antenna device may be statically tunedto provide a specific phase shift of an input RF signal. Alternatively,each unit cell may be modeled to include a lumped impedance element with(at least) one input and (at least) one output. The input(s) may bedynamically manipulated during operation to dynamically shift the phaseof an input signal in real-time from a selectable set of phase shifts.

In one example, network of tunable impedance elements 110 can be aspatially-periodic arrangement of tunable impedance elements, withspatial periodicity in at least one spatial dimension being less thanone-half of free-space wavelength. In another example, the specialdimension can be in two special dimensions or in three specialdimensions.

As previously described, the system may be modeled to include lumpedimpedance elements that can be passive, active, or variablypassive-active. At a given frequency, each impedance element may befully described by the complex value of its impedance “z.” A positiveinteger N may be used to describe the number of tunable or variablelumped impedance elements. A diagonal square matrix of size N may havediagonal elements z_(n) representative of the nth impedance element.Alternatively, an N-dimensional complex vector, {z_(n)}, can be used torepresent the n-valued list of impedance values.

Each variable impedance element may be modeled as a port (e.g., a lumpedport and/or a wave port). A plurality of lumped ports, N, may include aplurality of lumped input ports, with impedance values corresponding tothe impedance values of each of the variable impedance elements, and atleast one lumped external port, N_(e), that may or may not have avariable impedance or any impedance at all. That is, the z value of themodeled lumped external port, N_(e), may be zero and represent anidealized shorted port. Alternatively, the z value of the modeled lumpedexternal port, N_(e), may be infinity and represent an idealized openport. In many embodiments, the z value of the external port, N_(e), maybe a complex value with a magnitude between zero and infinity.

Regardless of the impedance values of each of the lumped ports, N,including the lumped input ports, N_(i), and the at least one lumpedexternal port, N_(e), each of the lumped ports (or in some examples waveports) may have its own self-impedance and the network of ports may bedescribed by an N×N impedance matrix (Z-Matrix) or by the equivalentinverse admittance matrix (Y-Matrix) where Y=Z⁻¹. Additionally, thenetwork of ports can be modeled as an S-parameter matrix or scatteringmatrix (S-Matrix). The Z-Matrix and its inverse the Y-Matrix areindependent from the specific z values of the ports because the matrixelements are defined as Z_(nm)=V_(n)/I_(m), where V_(n) and I_(m) arethe voltage at port n and the current at port m, measured with all otherports open. That is, assuming port currents I_(k)=0 for all k not equalto m or n. Similarly, for the admittance matrix, Y_(nm)=I_(m)/V_(n),measured with all other ports open. Again, that is assuming portcurrents I_(k)=0 for all k not equal to m or n.

The S-Matrix is expressible through the Z or Y matrices and the valuesof the lumped impedance elements as follows:

S=(√{square root over (y)}Z√{square root over (y)}−1)(√{square root over(y)}Z√{square root over (y)}+1)⁻¹=(1−√{square root over (z)}√{squareroot over (z)})(1+√{square root over (z)}Y√{square root over(z)})⁻¹  (1)

In the equation above, the “1” represents a unit matrix of size N. TheS-Matrix models the port-to-port transmission of off-diagonal elementsof the N-port network of impedance elements. In a lossless system, theS-Matrix is unitary. If elements s_(n) are the singular values of theS-Matrix, which are the same as the magnitudes of the eigenvalues, itcan be stated that in a lossless system, all s_(n)=1. In general, ifs_(max) is the largest singular value, then for a passive lossy systemit can be stated that s_(n)≤s_(max)≤1.

In an active system, these bounds still hold, however s_(max) can nowexceed unity, representing an overall power gain for at least onepropagation path. The Z and Y matrices are diagonalized in the samebasis represented by a unitary matrix U (U^(†)=U⁻¹), such thatZ=U^(†)Z_(d)U, Y=U^(†)Y_(d)U, where the subscript d indicates a diagonalmatrix, the elements of which are complex-valued eigenvalues of thecorresponding matrix.

Generally speaking, unless √{square root over (Z)} is proportional to aunit matrix (i.e., all lumped element impedances are equal), theS-Matrix will not be diagonal in the U-basis. In the U-basis, thegeneral form of the S-Matrix is S=U^(†)(1−ζY_(d)ζ)(1+ζY_(d)ζ)⁻¹U, wherea new non-diagonal matrix ζ=U√{square root over (z)}U^(†) is used suchthat √{square root over (z)}=U^(†)ζU, and Y_(d) is diagonal, though notgenerally commutative with ζ.

The S-Matrix of the system can be numerically evaluated with any desiredaccuracy by solving exactly N linear system problems (e.g.,Z_(nm)=V_(n)/I_(m) or Y_(nm)=I_(m)/V_(n) and the associated open portconditions described above). Such problems may be solved with FiniteElement Methods (FEM) or finite-difference time-domain (FDTD) basedsolvers for linear electromagnetic systems. Examples of commerciallyavailable solvers include ANSYS HFSS, COMSOL, and CST. These numericalsimulations incorporate various fine effects of the near-field andfar-field interactions between various parts of the system, regardlessof complexity.

The Z-Matrix and/or the Y-Matrix can be evaluated based on knowledge ofthe 5-matrix and the impedance values. With many FEM solvers, it is alsopossible to directly evaluate the Z-Matrix or the Y-Matrix, by solvingN² linear problems. This approach, however, is N times less efficientthan calculating the S-Matrix with a fixed set of port impedance values(known as reference impedance values), and transforming it to Z and/orY.

In one or more examples, each tunable impedance element of the networkof tunable impedance elements 110 can have a maximum dimension that isless than half of a wavelength of the smallest frequency within anoperating frequency range (e.g., between 0 to 18 GHz). One or more ofthe sub-wavelength tunable impedance elements may comprise a resonatingelement. In one or more examples, some or all of the sub-wavelengthtunable impedance elements may comprise metamaterials. In one or moreexamples, a network of tunable impedance elements (e.g., resonatingelements) may be collectively considered a metamaterial.

Network of tunable impedance elements 110 can have inter-elementspacings that are substantially less than a free-space wavelengthcorresponding to an operating frequency or frequency range. For example,the inter-element spacings may be less than one-half or one-quarter ofthe free-space operating wavelength. Network of tunable impedanceelements 110 may be configured to operate in a wide variety of operatingfrequency ranges, including, but not limited to, microwave frequencies(e.g., 0 to 18 GHz or any other frequency range). The presentlydescribed systems and methods may be adapted for use with otherfrequency bands, including those designated as very low frequency, lowfrequency, medium frequency, high frequency, very high frequency,ultra-high frequency, super-high frequency, and extremely high frequencyor millimeter waves.

Network of tunable impedance elements 110 can be connected to input port102, which can be a common transmission line (TL). Alternativewaveguides can be used instead of or in addition to TLs. A waveguide orTL may be modeled as another port in the S-Matrix, such as inHeretic-like architectures with variable couplers.

The impedance of each of the lumped impedance elements may be variablyadjusted through one or more impedance control inputs (tuning voltagevalues) received from controller 108, as will be described below.

In one or more examples, the lumped external port, N_(e), may comprise avirtual port, an external region of space assumed to be a void, a regionof space assumed to be filled with a dielectric material, and/or alocation in space assumed to be filled with a conductive, radiative,reactive, and/or reflective material.

The lumped external port, N_(e), may also be modeled as a virtualexternal port, comprising a field probe, as measured by a non-perturbingmeasurement. In other example, the virtual external port may represent anumerical field probe, as calculated using a numerical simulation.

In one or more examples, the impedance of each one of the network oftunable impedance elements 110 may be controlled individually, or onlysome of them may be variable. In any of the above embodiments, Ximpedance control inputs may be varied to control the impedance of Yimpedance elements, where X and Y are integers that may or may not beequal.

As a specific example, 1,000 unique impedance control inputs may beprovided for each of 1,000 unique impedance elements of the network oftunable impedance elements 110. Accordingly, each of the impedancecontrol inputs (tuning voltages) may be varied to control the impedanceof each of the impedance elements in network of tunable impedanceelements 110.

In some examples, one or more of the impedance control inputs (tuningvoltages) may utilize the application of a direct current (DC) voltageto variably control the impedance of the elements of network of tunableimpedance elements 110 based on the magnitude of the applied DC voltage.In other examples, an impedance control input may utilize one or more ofan electrical current input, a radiofrequency electromagnetic wave inputan optical radiation input, a thermal radiation input, a terahertzradiation input, an acoustic wave input, a phonon wave input, amechanical pressure input, a mechanical contact input, a thermalconduction input, an electromagnetic input, an electrical impedancecontrol input, and a mechanical switch input. In one or more examples,the lumped impedance elements may be modeled as two-port structures withan input and an output.

The lumped impedance elements may comprise one or more of a resistor, acapacitor, an inductor, a varactor, a diode, a Micro-Electro-MechanicalSystems (MEMS) capacitor, a Barium Strontium Benatate (BST) capacitor, atunable ferroelectric capacitor, a tunable MEMS inductor, a pin diode,an adjustable resistor, a High Electron Mobility Transistor (HEMT),and/or another type of transistor. Any of a wide variety of alternativecircuit components (whether in discrete or integrated form) may be partof a lumped impedance element (e.g., network of tunable impedanceelements 110).

One or more hardware, software, and/or firmware solutions may beemployed to perform operations for controlling an implementing a phaseshift of input signals using network of tunable impedance elements 110using phase shift module 100, as will be described below. For instance,a computer-readable medium (e.g., a non-transitory computer-readablemedium) may have instructions that are executable by a processor toprovide control voltages by controller 108 to tunable impedance elementsof network of tunable impedance elements 110. The executed operations ormethod steps may include determining a scattering matrix (S-Matrix) offield amplitudes for each tunable impedance element of network oftunable impedance elements 110.

As described above, S-Matrix is expressible in terms of an impedancematrix, Z-Matrix, with impedance values, z_(n), of each of eachimpedance element of network of impedance elements 110, N. Thus, bymodifying one or more of the impedance values, z_(n), associated withone or more of N impedance elements, a desired S-Matrix of fieldamplitudes can be attained.

Determining an optimized {z_(n)} may include calculating an optimizedZ-Matrix using one or more of a variety of mathematical optimizationtechniques. For example, the optimized {z_(n)} may be determined using aglobal optimization method involving a stochastic optimization method, agenetic optimization algorithm, a Monte-Carlo optimization method, agradient-assisted optimization method, a simulated annealingoptimization algorithm, a particle swarm optimization algorithm, apattern search optimization method, a Multistart algorithm, and/or aglobal search optimization algorithm. Determining the optimized {z_(n)}may be at least partially based on one or more initial guesses.Depending on the optimization algorithm used, the optimized values maybe local optimizations based on initial guesses and may not in fact betrue global optimizations. In other embodiments, sufficient optimizationcalculations are performed to ensure that a true globally optimizedvalue is identified. In some embodiments, a returned optimization valueor set of values may be associated with a confidence level or confidencevalue that the returned optimization value or set of values correspondsto global extrema as opposed to local extrema.

For gradient-assisted optimization, a gradient may be calculatedanalytically using an equation relating an S-parameter of the S-Matrixto the Z-Matrix and the optimized {z_(n)}. In some examples, a Hessianmatrix calculation may be utilized that is calculated analytically usingthe equation relating the S-parameter to the Z-Matrix and the optimized{z_(n)}. A quasi-Newton method may also be employed in some embodiments.In the context of optimization, the Hessian matrix may be considered amatrix of second derivatives of the scalar optimization goal functionwith respect to the optimization variable vector.

In some examples, the global optimization method may includeexhaustively or almost exhaustively determining all local extrema bysolving a multivariate polynomial equation and selecting a globalextrema from the determined local extrema. Alternative gradient-basedmethods may be used, such as conjugate gradient (CG) methods andsteepest descent methods, etc. In the context of optimization, agradient may be a vector of derivatives of the scalar optimization goalfunction with respect to the vector of optimization variables.

Exhaustively determining all local extrema may be performed by splittingthe domain based on expected roots and then splitting it into smallerdomains to calculate a single root or splitting the domain until adomain with a single root is found. Determining the optimized {z_(n)}may include solving the optimization problem in which a simple case mayinclude a clumped function scalar function with one output and N inputs.The N inputs could be complex z_(n) values and the optimized Z-Matrixmay be calculated based on an optimization of complex impedance valuesof the z_(n) vectors.

The optimized {z_(n)} may be calculated by finding an optimized Z-Matrixbased on an optimization of complex impedance values z_(n). Theoptimized {z_(n)} may be calculated by finding an optimized Z-Matrixbased on an optimization of roots of complex values of the impedancevalues z_(n). The optimized {z_(n)} may be calculated by finding anoptimized Z-Matrix based on an optimization of reactances associatedwith the impedance values of the impedance values z_(n). The optimized{z_(n)} may be calculated by finding an optimized Z-Matrix based on anoptimization of resistivities associated with the impedance values ofthe impedance values z_(n). The optimization may be constrained to allowonly positive or inductive values of reactances, or only negative orcapacitive values of reactances. In other embodiments, the optimizationof resistivities may be constrained to only allow for positive orpassive values of resistivities.

The optimized {z_(n)} may be calculated by finding an optimized Z-Matrixbased on an optimization of the impedance control inputs associated withthe lumped impedance elements of each of the sub-wavelength antennaelements. The optimized {z_(n)} may be calculated by optimizing anonlinear function. The nonlinear function may relate impedance valuesfor each of the lumped antenna ports, N_(a), as modeled in the S-Matrixand the associated impedance control inputs. In some embodiments, thenonlinear function may be fitted to a lower-order polynomial foroptimization.

Mapping the Z-Matrix values to the S-Matrix values may comprise anon-linear mapping. In some instances, the mapping may be expressible asa single- or multivariate polynomial. The polynomial may be of arelatively low order (e.g., 1-5). The S-Matrix may comprise N values andthe Z-Matrix may comprise M values, where N and M are both integers andequal to one another, such that there is a 1:1 mapping of S-Matrixvalues and Z-Matrix values. Any of a wide variety of mappings ispossible. For example, the S-Matrix may comprise N values and theZ-Matrix may comprise M values, where N squared is equal to M.Alternatively, there may be a 2:1 or 3:1 mapping or a 1:3 or 2:1mapping.

The physical location of the at least one lumped external port, N_(e),may be associated with a single-path or multipath propagation channelthat is electromagnetically reflective and/or refractive. The multipathpropagation channel may be in the near-field. In a radiative near-field,the multipath propagation pattern may be in the reactive near-field.

Determining the optimized {z_(n)} of impedance values for network oftunable impedance elements 110 may include determining an optimized setof control values for the plurality of impedance control inputs thatresults in an field amplitude for the at least one lumped external port,N_(e), in the S-Matrix that approximates the target field amplitude fora given operating frequency or frequency range.

The S-Matrix element S_(1N) represents the complex magnitude of field(e.g., electric field) at a particular location in space, given by theradius vector {right arrow over (r₀)}, normalized to the field magnitudeat the input port. The absolute value |S_(1N)|, or the morealgebraically convenient quantity |S_(1N)|², quantifies the quality offield concentration at that point. Maximizing this quantity (orminimizing in the case of forming nulls) represents a generalized phaseshifting algorithm.

To find all local optima and the global optimum we can use the equationq_(n)≡√{square root over (z)}_(n), which characterizes the individualport impedances z_(n). The equation above, S=U{right arrow over(r₀)}(1−ζY_(d)ζ)(1+ζY_(d)ζ)⁻¹U, is a rational (and meromorphic)analytical function of {q_(n)}.

To make this function bounded, and find its maxima that are attainablein a passive system, the function may be restricted to themultidimensional segment satisfying Re(z_(n))≥0, n=1, . . . , N.Equivalently, this condition is −π/2≤arg z_(n)≤π/2, and consequently−π/4≤arg q_(n)≤π/4.

To reduce this problem to real values, each q_(n) variable can beexpressed through real variables, q_(n)=ρ_(n)+ξ_(n). In this manner, thereal valued function |S_(1N)|² is now a function of 2N real variablesρ_(n),ξ_(n), which is a rational function comprising a ratio of two2N-variate polynomials.

In some examples, the resistance of each lumped element can be neglectedby assuming Re(z_(n))=0, z_(n)=ix_(n), with the real reactance valuesx_(n). In some examples, the system as a whole is still assumed passiveand lossy with the losses occurring on the paths between the ports andincorporated into the Z-Matrix (or Y-Matrix). This approximationsatisfies the passivity constraints and also reduces the number ofvariables to N because √zY√z→i→i√xY√x, and x is purely real.

The function |S_(1N)|² is necessarily bounded for a passive system, andtherefore it has a finite global maximum as a function of real-valuedvariables ρ_(n),ξ_(n). Moreover, it has a finite number of localextrema. These extrema can be found by solving a set of 2N multivariatepolynomial equations given by the standard zero gradient condition atthe extremum:

$\begin{matrix}{{\frac{\partial{s_{1N}}^{2}}{\partial\rho_{n}} = 0},\mspace{11mu}{\frac{\partial{s_{1N}}^{2}}{\partial\xi_{n}} = 0}} & (2)\end{matrix}$

With n=1, . . . , N.

In the simplified approach above, there are N unknowns χ_(n)=√x_(n) andN extremum conditions, so

$\begin{matrix}{\frac{\partial{s_{1N}}^{2}}{\partial\chi_{n}} = 0} & (3)\end{matrix}$

With n=1, . . . , N.

Once these extrema are found, the extremal values of the function areevaluated numerically, and the global maximum is determined by choosingthe largest local maximum. A similar approach can be performed toidentify one or more minimums to attain a target radiation pattern witha null at one or more specific radius vectors {right arrow over (r₀)}.

Numerical and symbolic-manipulation algorithms exist that take advantageof the polynomial nature of the resulting equations. For example,Wolfram Mathematica™ function Maximize supports symbolic solving of theglobal optimization problem for multivariate polynomial equations,unconstrained or with multivariate polynomial constraints. This functionis based on a Groebner-basis calculation algorithm, which reduces themultidimensional polynomial system to a triangular system, which is thenreduced to a single scalar polynomial equation by back-substitution.Similar functionality exists in other software packages, includingMATLAB™ with Symbolic Math Toolbox™, Maple™ and so on.

As previously discussed, once values are determine for each of the z_(n)for the variable or tunable impedance elements of network of tunableimpedance elements 110, each of the impedance elements can be tuned. Insome examples, the tuning is static and the impedance values are set atthe manufacturing stage. In other examples, a physical stimulus (e.g.,mechanical, electric, electromagnetic, and/or a combination thereof) maybe used to dynamically tune impedance elements to dynamically modify theradiation pattern of the antenna system during operation.

Depending on the manufacturing techniques employed (e.g., 3D printing)the calculated values of optimum impedance values may translatetrivially into the choices made for the selectable impedance elements.In contrast, for the dynamically adjustable, variable, or tunableimpedance elements, there is generally a non-trivial relationshipbetween the complex impedance of the elements and the stimuli thatcontrol them. In some embodiments, the relationship between the compleximpedance of the impedance elements and the control inputs may be basedon a magnitude of an applied signal. Appreciating that the magnitude ofthe stimulus may be binary in some embodiments (i.e., on or off), therelationship may be modeled as z_(n)=ƒ_(n)(s_(n)), where s_(n), is thereal-valued magnitude of the stimulus. The function ƒ_(n)(s_(n)) can befitted with a polynomial order S, and substituted into |S_(1N)|². Thefunctions ƒ_(n) can be all the same when identical dynamically tunableelements are used, in which case there will be N extremum conditions forN real variables s_(n), each of which is still a rational function.

In the lowest-order approximation, the fitting polynomial can be linear(S=1), in which case the complexity of the extremum problem is still

$\begin{matrix}{\frac{\partial{s_{1N}}^{2}}{\partial\chi_{n}} = 0} & (3)\end{matrix}$

With n=1, . . . , N.

The quality of a polynomial approximation depends greatly on thepractically available range of the stimulus, or the range chosen forother practical considerations. Because the s_(n) variables arerestricted to a finite interval, the optimization problem can be solvedwith the corresponding constraints. When the optimization problem issolved by exhaustive enumeration of the extrema, these constrains areapplied trivially and the local extrema not satisfying the constraintsare excluded from the enumeration.

As previously described, tunable impedance elements of network oftunable impedance elements 110 may have inter-element spacings that aresubstantially less than a free-space wavelength corresponding to anoperating frequency of phase shift module 100. For example, theinter-element spacings may be less than one-half or one-quarter of thefree-space operating wavelength. As shown, a common TL (via input port102) may be coupled to network of tunable impedance elements. Eachimpedance element of network of impedance elements 110 may have avariable impedance value that is set during manufacture or that can bedynamically tuned via one or more control inputs.

FIG. 3B illustrates a close-up view of a single tunable impedanceelement of network of tunable impedance elements of FIG. 1, according toan aspect of the present disclosure. In the close-up view 350, tunableimpedance value z_(n), 365, of a tunable impedance element 360 ofnetwork of tunable impedance elements 110 can have an impedance controlinput 370, through which a corresponding tuning voltage (voltage controlsignal) is received from controller 108, as will be described below.Impedance control input 370 can be used to control or vary the impedanceof the lumped impedance element, z_(n), 365 to achieve a desired phaseshift indicated by a phase shift input value.

FIG. 4 is a flow chart of a method of operation of the phase shiftmodule, according to one aspect of the present disclosure. FIG. 4 willbe described from the perspective of phase shift module 100. However,one or more specific steps are performed by controller 108 of phasemodule 100 while one or more other specific steps are performed bynetwork of tunable impedance elements 110, as will be described below.

At S400, phase shift module 100 receives an input signal. As describedabove, the input signal can be a continuous-wave signal having aparticular magnitude and/or frequency. The input signal can be acontinuous-wave radio frequency (RF) signal.

At S405, phase shift module 100 receives the magnitude and/or frequencyof the input signal. In one example, phase shift module 100 receivesonly the magnitude or the frequency of the input signal. In anotherexample, phase shift module 100 receives both the magnitude andfrequency of the input signal. In another example, phase shift moduledoes not receive any one of the magnitude or frequency of the inputsignal. In such case, step S405 is not performed.

In one example, upon receiving input signal at S400, phase shift module100, via controller 108, determines the magnitude (e.g., localmagnitudes of the input signal) and frequency of the input signalaccording to any known or to be developed method.

At S410, phase shift module 100 receives a phase shift input value. Asdescribed above, the phase shift input value is a desired value by whichthe phase of the input signal is to be shifted. In one example, thephase shift input value is received at controller 108 via control port104.

In one example, the phase shift module 100 has an array of possible(available) phase shift values stored thereon (e.g., stored on a memoryassociated with controller 108). This array or set of possible phaseshift values can be a finite set. Accordingly in one example, phaseshift module, via controller 108, receives a digital input (an integerinput) that corresponds to an index of one phase shift input value ofthe set stored in phase shift module 100. Based on the received integerinput (index), phase shift module 100 determines the corresponding phaseshift input value to be used.

In one example, the set possible phase shift input values has 2^(N)possible phase shift values, where N is a number of tunable impedanceelements of network of tunable impedance elements 110.

In one example, phase shift module 100 can be a 1 bit phase shifter andtherefore, the finite set of possible phase shift values has only twopossible phase shift values (e.g., 1 or 0).

At S415, phase shift module 100, via controller 108, determines a set oftuning voltages (voltage control signals) for network of tunableimpedance elements 110 based on the phase shift input value received atS410.

In one example and as part of determining each tuning voltage forelements of network of impedance elements 110, controller 108 determinesthe corresponding tuning voltage for each tunable impedance element ofnetwork of tunable impedance elements 110 based on an approximation ofnetwork of tunable impedance elements 110 as a network of lumped ports,as described above, with characteristic impedances representingimpedance values of tunable impedance elements of the network.

In one example, controller 108 performs the approximation by determininga scattering matrix (S-Matrix) of the network of lumped ports for agiven set of characteristic impedances of lumped ports, as describedabove.

In one example, controller 108 determines the S-Matrix, as describedabove (e.g., equation (1)) and based on an impedance matrix of thenetwork of lumped ports and the characteristic impedances of the lumpedports.

In one example, controller 108 determines the corresponding tuningvoltage for each tunable impedance element of network of tunableimpedance elements 110 such that a magnitude of an output signal atoutput port 106 and the magnitude of the input signal at input port 102are substantially equal (e.g., a ratio between the magnitude of theoutput signal and the magnitude of the input signal, |S₂₁|, does notdevice from 1 by more than a threshold, where the threshold can be anyvalue such as 1 dB, 3 dB, etc.).

In one example, controller 108 determines the corresponding tuningvoltage for each tunable impedance element of network of tunableimpedance elements 110 such that a ratio of a magnitude of an outputsignal at output port 106 to the magnitude of the input signal at inputport 102, |S₂₁|, is constant.

In one example, controller 108 determines the corresponding tuningvoltage for each tunable impedance element of network of tunableimpedance elements 110 such that a ratio of a magnitude of an outputsignal at output port 106 to the magnitude of the input signal at inputport 102, |S₂₁|, is greater than any one of 0.7, 0.8 or 0.9 for allpossible/available phase shift input values of phase shift module 110.

In another example, at S415, phase shift module 100, via controller 108,determines a set of tuning voltages for network of tunable impedanceelements 110 based on the phase shift input value received at S410 andthe frequency of the input signal received at S405. For example,controller 108 determines a corresponding tuning voltage to be suppliedto each tunable impedance element of network of tunable impedanceelements 110 based on a dependency of impedances of tunable impedanceelements and impedances of non-tunable branches of network of thenetwork of tunable impedance elements 110 on the frequency of the inputsignal.

In another example, phase shift module 100, via controller 108,determines a set of tuning voltages for network of tunable impedanceelements 110 based on the phase shift input value received at S410 andthe magnitude of the input signal received at S405. For example,controller 108 determines a corresponding tuning voltage to be suppliedto each tunable impedance element of network of tunable impedanceelements 110 based on a dependency of impedances of tunable impedanceelements and impedances of non-tunable branches of network of thenetwork of tunable impedance elements 110 on the local magnitude of RFvoltage or current of the input signal.

In another example, phase shift module 100, via controller 108,determines a set of tuning voltages for network of tunable impedanceelements 110 based on the phase shift input value received at S410 andthe frequency and the magnitude of the input signal received at S405.the local magnitude of RF voltage or current of the input signal.

After determining, at S415, tuning voltages for impedance elements ofnetwork of impedance elements 110, at S420, controller 108 sends thedetermined tuning voltage to corresponding impedance elements of networkof impedance elements 110 via corresponding control lines 206 of FIG. 2.

At S425, network of impedance elements 110 implements a phase shiftprocess for shifting the phase of the input signal according to thephase shift input value using the received tuning voltages.

At S430, phase shift module 100 outputs the phase shifted input signalas an output signal at output port 106.

Having described various examples of structure and operation of phaseshift module 100, it should be noted that phase shift module 100 canhave many different applications including but not limited to, anantenna system.

For clarity of explanation, in some instances the present technology maybe presented as including individual functional blocks includingfunctional blocks comprising devices, device components, steps orroutines in a method embodied in software, or combinations of hardwareand software.

Methods according to the above-described examples can be implementedusing computer-executable instructions that are stored or otherwiseavailable from computer readable media. Such instructions can comprise,for example, instructions and data which cause or otherwise configure ageneral purpose computer, special purpose computer, or special purposeprocessing device to perform a certain function or group of functions.Portions of computer resources used can be accessible over a network.The computer executable instructions may be, for example, binaries,intermediate format instructions such as assembly language, firmware, orsource code. Examples of computer-readable media that may be used tostore instructions, information used, and/or information created duringmethods according to described examples include magnetic or opticaldisks, flash memory, USB devices provided with non-volatile memory,networked storage devices, and so on.

Devices implementing methods according to these disclosures can comprisehardware, firmware and/or software, and can take any of a variety ofform factors. Typical examples of such form factors include laptops,smart phones, small form factor personal computers, personal digitalassistants, rackmount devices, standalone devices, and so on.Functionality described herein also can be embodied in peripherals oradd-in cards. Such functionality can also be implemented on a circuitboard among different chips or different processes executing in a singledevice, by way of further example.

The instructions, media for conveying such instructions, computingresources for executing them, and other structures for supporting suchcomputing resources are means for providing the functions described inthese disclosures.

Although a variety of examples and other information was used to explainaspects within the scope of the appended claims, no limitation of theclaims should be implied based on particular features or arrangements insuch examples, as one of ordinary skill would be able to use theseexamples to derive a wide variety of implementations. Further andalthough some subject matter may have been described in languagespecific to examples of structural features and/or method steps, it isto be understood that the subject matter defined in the appended claimsis not necessarily limited to these described features or acts. Forexample, such functionality can be distributed differently or performedin components other than those identified herein. Rather, the describedfeatures and steps are disclosed as examples of components of systemsand methods within the scope of the appended claims.

Claim language reciting “at least one of” refers to at least one of aset and indicates that one member of the set or multiple members of theset satisfy the claim. For example, claim language reciting “at leastone of A and B” means A, B, or A and B.

1. (canceled)
 2. A phase shifter, comprising: a network of tunableimpedance elements including tunable impedance elements in at least aportion of the network of tunable impedance elements that are staticallytuned to set a corresponding impedance value for each of the tunableimpedance elements; and an input port coupled to the network of tunableimpedance elements and configured to provide one or more input signalsto the network of tunable impedance elements that are shifted in phaseby the network of tunable impedance elements based, at least in part, oncorresponding statically tuned impedance values of the tunable impedanceelements.
 3. The phase shifter of claim 2, wherein each of the tunableimpedance elements is tuned one time as part of statically tuning thetunable impedance elements.
 4. The phase shifter of claim 2, whereineach of the tunable impedance elements is tuned during manufacturing ofthe network of tunable impedance elements.
 5. The phase shifter of claim2, wherein a corresponding statically tuned impedance value of a tunableimpedance element of the tunable impedance elements is statically tunedby: selecting one or more characteristics of the tunable impedanceelement for achieving the corresponding statically tuned impedancevalue; and manufacturing the tunable impedance element according to theone or more characteristics to achieve the corresponding staticallytuned impedance value at the tunable impedance element.
 6. The phaseshifter of claim 5, wherein the one or more characteristics include oneor more materials for fabricating the tunable impedance element.
 7. Thephase shifter of claim 5, wherein the one or more characteristics areselected to provide a specific phase shift to a specific radio frequencysignal through the network of tunable impedance elements.
 8. The phaseshifter of claim 2, wherein the network of tunable impedance elementshas non-negligible mutual coupling between at least one pair of tunableimpedance elements.
 9. The phase shifter of claim 2, wherein the networkof tunable impedance elements comprises an electromagnetic metamaterial.10. The phase shifter of claim 2, wherein the network of tunableimpedance elements comprises a spatially-periodic arrangement of tunableimpedance elements, with spatial periodicity in at least one spatialdimension being less than one-half of free-space wavelength.
 11. Thephase shifter of claim 10, wherein the spatial periodicity is in onespatial dimension.
 12. The phase shifter of claim 10, wherein thespatial periodicity is in two spatial dimensions.
 13. The phase shifterof claim 10, wherein the spatial periodicity is in three spatialdimensions.
 14. The phase shifter of claim 2, wherein the phase shifteris a single-frequency device.
 15. The phase shifter of claim 2, whereinthe phase shifter is a single input-single output phase shifter.
 16. Thephase shifter of claim 2, wherein the phase shifter is afinite-operational bandwidth device with an operational frequencyselectable from an operational bandwidth range.
 17. A method comprising:statically tuning tunable impedance elements in at least a portion of anetwork of tunable impedance elements of a phase shifter to set acorresponding impedance value for each of the tunable impedanceelements; and providing one or more input signals to the network oftunable impedance elements through an input port to phase shift the oneor more input signals based, at least in part, on correspondingstatically tuned impedance values of the tunable impedance elements. 18.The method of claim 17, wherein each of the tunable impedance elementsis tuned one time as part of statically tuning the tunable impedanceelements.
 19. The method of claim 17, wherein each of the tunableimpedance elements is tuned during manufacturing of the network oftunable impedance elements.
 20. The method of claim 17, wherein acorresponding statically tuned impedance value of a tunable impedanceelement of the tunable impedance elements is statically tuned by:selecting one or more characteristics of the tunable impedance elementfor achieving the corresponding statically tuned impedance value; andmanufacturing the tunable impedance element according to the one or morecharacteristics to achieve the corresponding statically tuned impedancevalue at the tunable impedance element.
 21. The method of claim 20,wherein the one or more characteristics include one or more materialsfor fabricating the tunable impedance element.
 22. The method of claim20, wherein the one or more characteristics are selected to provide aspecific phase shift to a specific radio frequency signal through thenetwork of tunable impedance elements.
 23. The method of claim 17,wherein the network of tunable impedance elements has non-negligiblemutual coupling between at least one pair of tunable impedance elements.24. The method of claim 17, wherein the network of tunable impedanceelements comprises an electromagnetic metamaterial.
 25. The method ofclaim 17, wherein the network of tunable impedance elements comprises aspatially-periodic arrangement of tunable impedance elements, withspatial periodicity in at least one spatial dimension being less thanone-half of free-space wavelength.
 26. The method of claim 25, whereinthe spatial periodicity is in one spatial dimension.
 27. The method ofclaim 25, wherein the spatial periodicity is in two spatial dimensions.28. The method of claim 25, wherein the spatial periodicity is in threespatial dimensions.
 29. The method of claim 17, wherein the phaseshifter is a single-frequency device.
 30. The method of claim 17,wherein the phase shifter is a single input-single output phase shifter.31. The method of claim 17, wherein the phase shifter is afinite-operational bandwidth device with an operational frequencyselectable from an operational bandwidth range.